If the person proposing to your daughter is as you have described him, then it is not permissible for you to give her in marriage to him, because she is a trust in your hands, so it is incumbent for you to choose for her the most righteous man in his religion and his character.
It is not permissible for a person who does not pray to be married to a Muslim woman who does pray, since he is not a suitable match for her, because abandoning the prayer is an act of major disbelief, according to the saying of the Prophet sallallaahu alayhi was salam:
‘Between a man and polytheism and disbelief is the abandonment of prayer.’ (muslim no.82)
And the saying of the Prophet sallallaahu alayhi was salam:
‘The covenant between us and them is prayer; whoever abandons it has committed an act of disbelief.’ (At-tirmithi no. 2621)
Narrated by Imam Ahmad and the compilers of the Sunan, with an authentic chain of narrators.
There are many other evidences in the Book (of Allaah) and the Sunnah which prove the disbelief of one who abandons the prayer, even if he does not reject its obligation, according to the most correct of two opinions held by the scholars. However, if he rejects its obligation or mocked it, then he is guilty of major disbelief according to the consensus of the Muslims.
As for the one who drinks alcohol but prays, he is not guilty of disbelief by doing this, as long as he does not claim that it is permissible, but he has committed a major sin and he has gone astray thereby. Therefore, it is lawful for you not to give her in marriage to him, even if he prays, due to his sin and because he might lead his wife and children to this great crime.
We ask Allaah to improve the situation of the Muslims and guide them to His Straight Path, and to preserve us and them from obeying vain desires and Satan, for verily, He is Most Generous, Most Noble.